Question:
Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.
Correct Answer
$8720
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 6%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $5450 × 6% × 10
= $5450 ×6/100 × 10
= 5450 × 6 × 10/100
= 32700 × 10/100
= 327000/100
= $3270
Thus, Simple Interest = $3270
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $3270
= $8720
Thus, Amount to be paid = $8720 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $5450
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 10 years
Thus, Amount (A)
= $5450 + ($5450 × 6% × 10)
= $5450 + ($5450 ×6/100 × 10)
= $5450 + (5450 × 6 × 10/100)
= $5450 + (32700 × 10/100)
= $5450 + (327000/100)
= $5450 + $3270 = $8720
Thus, Amount (A) to be paid = $8720 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5450, the simple interest in 1 year
= 6/100 × 5450
= 6 × 5450/100
= 32700/100 = $327
Thus, simple interest for 1 year = $327
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $327 × 10 = $3270
Thus, Simple Interest (SI) = $3270
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $3270
= $8720
Thus, Amount to be paid = $8720 Answer
Similar Questions
(1) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 7% simple interest?
(2) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 5% simple interest.
(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 7 years.
(4) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 4 years.
(5) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.
(6) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 7 years.
(8) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12920 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 4 years.
(10) Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 8 years.